How Did Grievous Almost Become Force Sensitive and Dooku's Sith Apprentice?

In Legends, Dooku had the dying Grievous transfused with blood taken from the frozen corpse of Jedi Master Sifo-Dyas, whose blood was rich in midi-chlorians. The blood held Grievous together long enough for the Geonosians to rebuild him, but it produced no Force sensitivity whatsoever, and Grievous saw that as a personal failure. (The Eyes of Revolution; Unknown Soldier: The Story of General Grievous)

Dooku set the crash up#

Nothing about the accident was an accident. In Legends, the Kaleesh warlord had once worked for San Hill of the InterGalactic Banking Clan, commanding the Clan's droid enforcers, before walking out on the contract to fight the Huk again back home. Hill was furious, and he took the problem to his allies, Count Dooku and Darth Sidious. (Labyrinth of Evil; Unknown Soldier: The Story of General Grievous)

Hill, Dooku and the Geonosian leader Poggle the Lesser worked out something better than having him killed. They would cripple Grievous and rebuild him as a cyborg under their control. An ion bomb went aboard his shuttle Martyr, and his seat was rigged so that Dooku could eject him remotely when the charge went off rather than let him be vaporised. (The Eyes of Revolution; Unknown Soldier: The Story of General Grievous)

It worked. Grievous was mortally injured, and by the time Dooku reached the crash site he was already dying. A heart stun kept him alive just long enough to be shipped to Geonosis. While the body was in transit, Dooku made a detour to his own homeworld of Serenno to collect something he had been saving. (The Eyes of Revolution)

The blood of Sifo-Dyas#

Serenno was where Dooku kept the corpse of Sifo-Dyas, the Jedi Master who had been removed from the High Council for holding views the rest of them judged too extreme. Sifo-Dyas had once been Dooku's friend. The Pykes shot down his shuttle over a moon of Oba Diah on Tyranus's orders, and in Legends Dooku kept the body in cryogenic storage rather than dispose of it. (The Lost One; The Eyes of Revolution)

That corpse was still full of midi-chlorian rich blood, and Dooku used it to keep Grievous's body alive on the way to Geonosis. The hope it raised was simple enough: a body loaded with midi-chlorians from a powerful Jedi might find the Force following. (The Eyes of Revolution; Unknown Soldier: The Story of General Grievous)

It did not. The midi-chlorians helped save his life, which was no small thing given the state he was in, but they granted him nothing else. Grievous woke up with a Jedi's blood in him and no more connection to the Force than the battle droids he would go on to command. To San Hill and his partners the experiment was a triumph, because they had the general they wanted. To Grievous it was a personal failure. (Unknown Soldier: The Story of General Grievous)

What they built instead#

If he could not have the Force, they gave him everything else. On Geonosis, Poggle the Lesser's scientists implanted his brain and eyes into a duranium alloy body modelled on an ancient Krath war droid. The legs were LX-44 units with magnetised talons. The two electro-driven arms could split at the dislocating shoulders to make four, each hand carrying a pair of opposable thumbs. What was left of his organs went into a synthskin gut-sack sealed against vacuum. (Star Wars: Revenge of the Sith: The Visual Dictionary; The New Essential Guide to Droids)

They worked on the brain as well, and they did it against his wishes. The Geonosians trimmed away memories they judged disturbing, enhanced his rage centres, sharpened his equilibrium so he could use the new body's speed, and installed a kill-switch operated by Dooku personally. The finished product was faster, angrier and easier to control than the man who had gone into the operating theatre. (The New Essential Guide to Droids)

Grievous hated it. When Dooku handed him his new title of Supreme Commander of the Droid Armies along with his first lightsaber, which was Sifo-Dyas' own weapon, General Grievous responded by slaughtering every MagnaGuard in the room and shouting that he was not a droid. He then carved himself a new death mask in armorplast, modelled on the one he had inherited from his father, and had it grafted onto his alloy skull. (The Eyes of Revolution; Unknown Soldier: The Story of General Grievous)

Apprentice in name only#

Dooku trained him. Grievous says as much in Revenge of the Sith, telling Obi-Wan he was trained in the Jedi arts by Count Dooku, and Legends adds that he took to it quickly. Dooku taught him lightsaber combat personally and turned him into a genuinely dangerous duelist, good enough to fight Obi-Wan Kenobi more than once during the Clone Wars. (Revenge of the Sith; Labyrinth of Evil; Unknown Soldier: The Story of General Grievous)

Sith training was never on the table, because none of it works without the Force. What Dooku got was a weapon he could point at the Jedi Order and switch off if it turned on him, which is a useful thing for a Sith Lord who intends to eventually replace his own master. Under the Rule of Two, an apprentice is always calculating. Dooku kept a close watch on his general regardless, sending the Separatist officer Vulpus to observe him when Grievous started turning captured younglings into cyborgs of his own. (General Grievous)

The relationship stayed sour. After Grievous failed to kill Kit Fisto in his own castle, Dooku's assessment was that there was room for improvement, which is about as close to contempt as the Count ever got in public. (Lair of Grievous)

The lesson Palpatine took from it#

Dooku had spent enormous effort building a superior cyborg body and had ended up with a commander who resented his handlers and could only be controlled by a switch. (The New Essential Guide to Droids; The Eyes of Revolution)

When Palpatine came to rebuild what was left of Anakin Skywalker, Legends has the same droids that rebuilt Grievous do the work. Darth Vader's suit was nowhere near the machine that Grievous got. No four arms, no enhanced agility. Its linkages were faulty and needed constant maintenance, and the surgical droid DD-13 suspected Sidious allowed the flaws on purpose to keep Vader from rebelling. (Star Wars: Revenge of the Sith: The Visual Dictionary; Star Wars: Darth Vader: A 3-D Reconstruction Log)

Nobody in the story spells out the link, but it's a fair reading. The Grievous experiment failed at making a Force user, and Vader's suit looks like the work of a master who knew how much power he should never hand an apprentice. (Star Wars: Darth Vader: A 3-D Reconstruction Log)